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[SOLVED] eigenvalue and eigenfunction for Fredholm method

dwsmith

Well-known member
Feb 1, 2012
1,673
Given
\[
f(x) = \lambda\int_0^1xy^2f(y)dy
\]
At order \(\lambda^2\) and \(\lambda^3\), we have repeated zeros so
\[
D(\lambda) = 1 - \frac{\lambda}{4}.
\]
Then we have
\[
\mathcal{D}(x, y;\lambda) = xy^2
\]
so
\[
f(x) = \frac{\lambda}{D(\lambda)}\int_0^1\mathcal{D}(x, y;\lambda)dy.
\]
How do I get the eigenfunction and value from this method?